On two-dimensional classical and Hermite sampling

R. M. Asharabi, J. Prestin
2015 IMA Journal of Numerical Analysis  
We investigate some modifications of the two-dimensional sampling series with a Gaussian function for wider classes of bandlimited functions including unbounded entire functions on R 2 and analytic functions on a bivariate strip. The first modification is given for the twodimensional version of the Whittaker-Kotelnikov-Shannon sampling (classical sampling) and the second is given for two-dimensional sampling involving values of all partial derivatives of order α ≤ 2 (Hermite sampling). These
more » ... ifications improve the convergence rate of classical and Hermite sampling which will be of exponential type. Numerical examples are given to illustrate the advantages of the new method. AMS(2010): 94A20, 41A80, 41A25, 65L70
doi:10.1093/imanum/drv022 fatcat:y7cdbdy5pndchnujwlveddi5au